Volume of a Rectangular Shape with Slanted Sides

Calculator of how many milliliters, centiliters, deciliters or liters fit into a casserole dish or baking pan with a rectangular base and sloping sides.

This calculation assumes that the sides on the left, right, front, and back are equally inclined. Then the two rectangles at the bottom and at the top have the same ratio. Mathematically speaking, such a shape is a rectangular frustum. However, such a frustum or truncated pyramid is usually depicted with the larger rectangular area at the bottom, whereas this kitchen shape has the smaller rectangle as its closed base. In this kitchen shape, the upper rectangle of the mathematical shape is the opening.

Example: A baking pan has a base that is 12 centimeters long and 8 centimeters wide. The opening measures 15 by 10 centimeters. The height is 6 centimeters. This pan holds 732 milliliters. If the fill level is 3 centimeters, meaning the pan is only filled to the middle, then it contains 325.5 milliliters. This is less than half, because the pan widens towards the top, but the smaller, lower part is filled.

Please enter three of the four values of length and width of the base and the opening. Also, enter the height and if needed the fill level. The fill level can be omitted, in that case, it will be considered equivalent to the height. Measurements are taken inside the shape. The volume in milliliters (ml), centiliters (cl), deciliters (dl) and in liters (l) will be calculated.

Length bottom:		cm
Width bottom:		cm
Length opening:		cm
Width opening:		cm
Height:		cm
Fill level:		cm
Volume:		ml
Volume:		cl
Volume:		dl
Volume:		l

This ovenproof casserole dish measures 28 by 19 centimeters at the opening. These dimensions are easier to measure than those at the bottom. The bottom is 24 centimeters long and 5 centimeters high. Therefore, this dish holds just under 2.3 liters. If the dish is filled to half its height, or 2.5 centimeters, it holds slightly more than one liter, 1061 milliliters to be precise.

If the dish is not completely filled, the size of the rectangle at the fill level must first be determined. With base values a and b, top values c and d, height h, and fill level f, the formula for its length and width is a+f/h*(c-a) and b+f/h*(d-b). With these values ​​instead of the top opening values and the fill level instead of the height, the formula for the rectangular frustum is then used for the calculation.

Last updated on 02/07/2026. Author: Jürgen Kummer

Here you can convert metric volume units into customary and imperial units.

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